Journal: SIAM Journal on Financial Mathematics

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SIAM

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1945-497X

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2010 - 2019132020 - 20257
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Publications 1 - 10 of 20
  • Hedging under an expected loss constraint with small transaction costs
    Item type: Journal Article
    Bouchard, Bruno; Moreau, Ludovic; Soner, Mete (2016)
    SIAM Journal on Financial Mathematics
  • Portfolio Selection with Small Transaction Costs and Binding Portfolio Constraints
    Item type: Journal Article
    Liu, Ren; Muhle-Karbe, Johannes (2012)
    SIAM Journal on Financial Mathematics
    An investor with constant relative risk aversion and an infinite planning horizon trades a risky and a safe asset with constant investment opportunities in the presence of small transaction costs and a binding exogenous portfolio constraint. We explicitly derive the optimal trading policy, its welfare, and implied trading volume. As an application, we study the problem of selecting a prime broker among alternatives with different lending rates and margin requirements. Moreover, we discuss how changing regulatory constraints affect the deposit rates offered for illiquid loans.
  • Optimal Portfolio Liquidation with Execution Cost and Risk
    Item type: Journal Article
    Kharroubi, Idris; Pham, Huyên (2010)
    SIAM Journal on Financial Mathematics
  • A Stochastic Partial Differential Equation Model for Limit Order Book Dynamics
    Item type: Journal Article
    Cont, Rama; Müller, Marvin Sebastian (2021)
    SIAM Journal on Financial Mathematics
    We propose an analytically tractable class of models for the dynamics of a limit order book, described through a stochastic partial differential equation with multiplicative noise for the order book centered at the mid-price, along with stochastic dynamics for the mid-price which is consistent with the order flow dynamics. We provide conditions under which the model admits a finite-dimensional realization driven by a (low-dimensional) Markov process, leading to efficient methods for estimation and computation. We study two examples of parsimonious models in this class: a two-factor model and a model in which the order book depth is mean reverting. For each model we perform a detailed analysis of the role of different parameters, study the dynamics of the price, order book depth, volume, and order imbalance, provide an intuitive financial interpretation of the variables involved, and show how the model reproduces statistical properties of price changes, market depth, and order flow in limit order markets. © 2021, Society for Industrial and Applied Mathematics
  • Short Communication: Inversion of Convex Ordering: Local Volatility Does Not Maximize the Price of VIX Futures
    Item type: Journal Article
    Acciaio, Beatrice; Guyon, Julien (2020)
    SIAM Journal on Financial Mathematics
    It has often been stated that, within the class of continuous stochastic volatility models calibrated to vanillas, the price of a VIX future is maximized by the Dupire local volatility model. In this article we prove that this statement is incorrect: we build a continuous stochastic volatility model in which a VIX future is strictly more expensive than in its associated local volatility model. More generally, in our model, strictly convex payoffs on a squared VIX are strictly cheaper than in the associated local volatility model. This corresponds to an inversion of convex ordering between local and stochastic variances, when moving from instantaneous variances to squared VIX, as convex payoffs on instantaneous variances are always cheaper in the local volatility model. We thus prove that this inversion of convex ordering, which is observed in the S&P 500 market for short VIX maturities, can be produced by a continuous stochastic volatility model. We also prove that the model can be extended so that, as suggested by market data, the convex ordering is preserved for long maturities. © 2020, Society for Industrial and Applied Mathematics
  • Merton problem with taxes
    Item type: Journal Article
    BenTahar, Imen; Soner, Mete; Touzi, Nizar (2010)
    SIAM Journal on Financial Mathematics
  • A Multifactor Polynomial Framework for Long-Term Electricity Forwards with Delivery Period
    Item type: Journal Article
    Kleisinger-Yu, Xi; Komaric, Vlatka; Larsson, Martin; et al. (2020)
    SIAM Journal on Financial Mathematics
    We propose a multifactor polynomial framework to model and hedge long-term electricity contracts with delivery period. This framework has several advantages: the computation of forwards, risk premium, and correlation between different forwards is fully explicit, and the model can be calibrated to observed electricity forward curves easily and well. Electricity markets suffer from nonstorability and poor medium- to long-term liquidity. Therefore, we suggest a rolling hedge which only uses liquid forward contracts and is risk-minimizing in the sense of Föllmer and Schweizer. We calibrate the model to over eight years of German power calendar year forward curves and investigate the quality of the risk-minimizing hedge over various time horizons. © 2020 Society for Industrial and Applied Mathematics.
  • Optimal make-take fees in a multi market-maker environment
    Item type: Journal Article
    Baldacci, Bastien; Possamaï, Dylan; Rosenbaum, Mathieu (2021)
    SIAM Journal on Financial Mathematics
    Following the recent literature on make-take fees policies, we consider an exchange wishing to set a suitable contract with several market makers in order to improve trading quality on its platform. To do so, we use a principal-agent approach, where the agents (the market makers) optimize their quotes in a Nash equilibrium fashion, providing best response to the contract proposed by the principal (the exchange). This contract aims at attracting liquidity on the platform. This is because the wealth of the exchange depends on the arrival of market orders, which is driven by the spread of market makers. We compute the optimal contract in quasi-explicit form and also derive the optimal spread policies for the market makers. Several new phenomena appears in this multi market-maker setting. In particular we show that it is not necessarily optimal to have a large number of market makers in the presence of a contracting scheme.
  • A Mean-Field Game of Market-Making against Strategic Traders
    Item type: Journal Article
    Baldacci, Bastien; Bergault, Philippe; Possamaï, Dylan (2023)
    SIAM Journal on Financial Mathematics
    We design a market-making model à la Avellaneda and Stoikov [Quant. Finance, 8 (2008), pp. 217–224] in which the market-takers act strategically, in the sense that they design their trading strategy based on an exogenous trading signal. The market-maker chooses her quotes based on the average market-takers’ behavior, modelled through a mean-field interaction. We derive, up to the resolution of a coupled HJB-Fokker–Planck system, the optimal controls of the market-maker and the representative market-taker. This approach is flexible enough to incorporate different behaviors for the market-takers and takes into account the impact of their strategies on the price process.
  • Discrete Time Term Structure Theory and Consistent Recalibration Models
    Item type: Journal Article
    Richter, Anja; Teichmann, Josef (2017)
    SIAM Journal on Financial Mathematics
Publications 1 - 10 of 20